Statistical Reliability with Applications

This chapter reviews fundamental ideas in reliability theory and inference. The first part of the chapter accounts for lifetime distributions that are used in engineering reliability analyis, including general properties of reliability distributions that pertain to lifetime for manufactured products. Certain distributions are formulated on the basis of simple physical properties, and other are more or less empirical. The first part of the chapter ends with a description of graphical and analytical methods to find appropriate lifetime distributions for a set of failure data. The second part of the chapter describes statistical methods for analyzing reliability data, including maximum likelihood estimation and likelihood ratio testing. Degradation data are more prevalent in experiments in which failure is rare and test time is limited. Special regression techniques for degradation data can be used to draw inference on the underlying lifetime distribution, even if failures are rarely observed. The last part of the chapter discusses reliability for systems. Along with the components that comprise the system, reliability analysis must take account of the system configuration and (stochastic) component dependencies. System reliability is illustrated with an analysis of logistics systems (e.g., moving goods in a system of product sources and retail outlets). Robust reliability design can be used to construct a supply chain that runs with maximum efficiency or minimum cost

Bayesian Network Approach to Assessing System Reliability for Improving System Design and Optimizing System Maintenance

abstract: A quantitative analysis of a system that has a complex reliability structure always involves considerable challenges. This dissertation mainly addresses uncertainty in- herent in complicated reliability structures that may cause unexpected and undesired results. The reliability structure uncertainty cannot be handled by the traditional relia- bility analysis tools such as Fault Tree and Reliability Block Diagram due to their deterministic Boolean logic. Therefore, I employ Bayesian network that provides a flexible modeling method for building a multivariate distribution. By representing a system reliability structure as a joint distribution, the uncertainty and correlations existing between system’s elements can effectively be modeled in a probabilistic man- ner. This dissertation focuses on analyzing system reliability for the entire system life cycle, particularly, production stage and early design stages. In production stage, the research investigates a system that is continuously mon- itored by on-board sensors. With modeling the complex reliability structure by Bayesian network integrated with various stochastic processes, I propose several methodologies that evaluate system reliability on real-time basis and optimize main- tenance schedules. In early design stages, the research aims to predict system reliability based on the current system design and to improve the design if necessary. The three main challenges in this research are: 1) the lack of field failure data, 2) the complex reliability structure and 3) how to effectively improve the design. To tackle the difficulties, I present several modeling approaches using Bayesian inference and nonparametric Bayesian network where the system is explicitly analyzed through the sensitivity analysis. In addition, this modeling approach is enhanced by incorporating a temporal dimension. However, the nonparametric Bayesian network approach generally accompanies with high computational efforts, especially, when a complex and large system is modeled. To alleviate this computational burden, I also suggest to building a surrogate model with quantile regression. In summary, this dissertation studies and explores the use of Bayesian network in analyzing complex systems. All proposed methodologies are demonstrated by case studies.Dissertation/ThesisDoctoral Dissertation Industrial Engineering 201

A RISK-INFORMED DECISION-MAKING METHODOLOGY TO IMPROVE LIQUID ROCKET ENGINE PROGRAM TRADEOFFS

This work provides a risk-informed decision-making methodology to improve liquid rocket engine program tradeoffs with the conflicting areas of concern affordability, reliability, and initial operational capability (IOC) by taking into account psychological and economic theories in combination with reliability engineering. Technical program risks are associated with the number of predicted failures of the test-analyze-and-fix (TAAF) cycle that is based on the maturity of the engine components. Financial and schedule program risks are associated with the epistemic uncertainty of the models that determine the measures of effectiveness in the three areas of concern. The affordability and IOC models' inputs reflect non-technical and technical factors such as team experience, design scope, technology readiness level, and manufacturing readiness level. The reliability model introduces the Reliability- As-an-Independent-Variable (RAIV) strategy that aggregates fictitious or actual hotfire tests of testing profiles that differ from the actual mission profile to estimate the system reliability. The main RAIV strategy inputs are the physical or functional architecture of the system, the principal test plan strategy, a stated reliability-bycredibility requirement, and the failure mechanisms that define the reliable life of the system components. The results of the RAIV strategy, which are the number of hardware sets and number of hot-fire tests, are used as inputs to the affordability and the IOC models. Satisficing within each tradeoff is attained by maximizing the weighted sum of the normalized areas of concern subject to constraints that are based on the decision-maker's targets and uncertainty about the affordability, reliability, and IOC using genetic algorithms. In the planning stage of an engine program, the decision variables of the genetic algorithm correspond to fictitious hot-fire tests that include TAAF cycle failures. In the program execution stage, the RAIV strategy is used as reliability growth planning, tracking, and projection model. The main contributions of this work are the development of a comprehensible and consistent risk-informed tradeoff framework, the RAIV strategy that links affordability and reliability, a strategy to define an industry or government standard or guideline for liquid rocket engine hot-fire test plans, and an alternative to the U.S. Crow/AMSAA reliability growth model applying the RAIV strategy

Bayesian nonparametric system reliability using sets of priors

An imprecise Bayesian nonparametric approach to system reliability with multiple types of components is developed. This allows modelling partial or imperfect prior knowledge on component failure distributions in a flexible way through bounds on the functioning probability. Given component level test data these bounds are propagated to bounds on the posterior predictive distribution for the functioning probability of a new system containing components exchangeable with those used in testing. The method further enables identification of prior–data conflict at the system level based on component level test data. New results on first-order stochastic dominance for the Beta-Binomial distribution make the technique computationally tractable. Our methodological contributions can be immediately used in applications by reliability practitioners as we provide easy to use software tools

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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